With recurrent pregnancy loss I honestly would only do IVF if you combine it with PGS/genetic screening. You'll get much more valuable information out of the process. Otherwise it wouldn't be worth it in my opinion.
However they have tested materials from your previous pregnancy, right? And didn't find anything abnormal? PGS primarily helps find embryos that are genetically normal and can hopefully survive preganancy but I thought you had more of an issue with your body itself fighting the pregnancy. PGS probably won't help with that. But like I said you'll get much more valuable info and be able to cross off one possibility of what could be causing your issues.
I have no clue how they handle genetic screening in the U.K. but it's pretty standard here now and it adds about $5,000 to the process which comparatively speaking isn't ton. So if you can get one cycle paid for and still need to pay for genetic testing out of pocket, it can be doable.